You can see if a restore to a recent backup will recover the information.

Open iTunes, attach your iPhone, right click on the iPhone icon in the left column of iTunes and select Restore From Backup.

Select the most recent backup and restore.

Your iPhone will restore and then reboot.

Upon restore see if the contacts are present that were missing.

If the contacts are not on the backup you selected, select a different backup.

If either no backups are available or none of the backups have your contacts/notes/calendar, there is likely no way to recover the information.

As far as apps/music/videos are concerned, you can recover these if they were purchased in iTunes by going to (on your iPhone) App Store-> Updates (on bottom right) -> Purchases -> Not on this iPhone and then redownload the apps (no cost) --- For music/movies, you can go to iTunes app on your iPhone -> Purchased (on bottom right) -> Not on this iPhone and then redownload the music/movies purchased.

Pictures would be stored in a "backup" as stated above (with contacts/calendars/notes/etc.).

Any non-iTunes purchased items are likely lost, unless they are on your computer's iTunes. You can sync these items by going to the iPhone icon in the left column of iTunes, then going to each tab (music, movies, pictures, etc.) and checking "Sync ...." (i.e. Sync Music) on each tab and clicking Sync/Apply in the bottom right of the iTunes window.

Update me on the results. Let me know if you need further assistance. Good luck!

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